Mailman 3 July 2018 - Kwant-discuss

Gate-defined Nanowire Quantum Dot
by Jonathan Fields Sept. 15, 2022

Sept. 15, 2022

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

4 4

How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

3 3

Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

3 3

How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

Dear Sir, I am a PhD student of Hong Kong University of Science and Technology. I want to use KWANT to caculate Hall resistance of a Hall bar structure.We can get the conductance between 6 electrodes, but how to get hall resistance? Can you give me some help? Thank you very much. Best Regards, Zhang Bing

4 3

Onsite and hopping values in QHE
by elchatz＠auth.gr Sept. 15, 2018

Sept. 15, 2018

Hello everyone, I am trying to reproduce the QHE bar device calculations http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pum… However, I am having difficulty with the onsite and hopping values as I am using TBModels https://github.com/Z2PackDev/TBmodels and therefore the values are not the same for all sites. The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the position-dependent Hamiltonian. I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memory-efficient. I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of. Regards -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

2 7

Calculating valley polarized conductances using Kwant
by Kevin Ryczko Aug. 1, 2018

Aug. 1, 2018

Dear community, I would like to calculate the valley polarized conductance for a graphene nanoribbon with 2 leads (let’s say in the x-direction). My current approach is this: 1) Get the S-matrix for a certain energy 2) Find the indices of the modes with positive velocities 3) Separate these modes by positive and negative momenta 4) Get the sub matrix from the S-matrix 5) Sum the transmission coefficients for positive and negative momenta The code below illustrates these 5 steps: import progressbar def valleyPolarizability(syst, energies, lead_start=0, lead_end=1): KPs = [] Ks = [] bar = progressbar.ProgressBar() for energy in bar(energies): smatrix = kwant.smatrix(syst, energy, params={'phi': phi}) positives = np.where(smatrix.lead_info[lead_start].velocities >= 0)[0] momentas = smatrix.lead_info[lead_start].momenta[positives] K_prime_indices = np.where(momentas < 0)[0] K_indices = np.where(momentas >= 0)[0] submatrix = smatrix.submatrix(lead_end, lead_start) K_prime_T = np.absolute(np.sum(submatrix[:, K_prime_indices]))**2 K_T = np.absolute(np.sum(submatrix[:, K_indices]))**2 KPs.append(K_prime_T) Ks.append(K_T) return KPs, Ks Could someone please let me know if this is the correct approach? Will the K_prime_indices and K_indices have the correct indexing in the sub matrix? Thanks, Kevin Ryczko

2 1

defining lattice for armchair graphene nanoribbon (AGNR)
by Arunabha Ghoshal July 30, 2018

July 30, 2018

Dear Kwant Developers, I am facing some difficulty in defining the lattice for armchair-edged graphene nanoribbon. To be specific, I am being unable to find out the ' prim_vecs' (primitive vectors) and the 'basis' (coordinates of basis sites) that I should provide to kwant.lattice.general(*prim_vecs*, *basis=None*, *name=''*) as parameter to obtain the lattice structure of armchair GNR. As per my understanding, I can find the lattice structure for zigzag-edged GNR by using either the following two approaches: > graphene = kwant.lattice.general([(1, 0), (sin_30, cos_30)], [(0, 0), (0, 1 / sqrt(3))]) or > graphene= kwant.lattice.honeycomb(a=1, name=’‘, norbs=None) But I am failing to define the lattice structure for the armchair-edged graphene nanoribbon. Moreover, as per my understanding, the distance between two adjacent atoms (C-C) in graphene is 0.142nm. So what value of 'a' should I provide in >graphene=kwant.lattice.honeycomb(a=1, name=’‘, norbs=None) to obtain the accurate lattice structure. In this context I would ask you to kindly guide me to find the solutions of the above mentioned queries. Thanking you Regards Arunabha Ghoshal

1 0

<no subject>
by Prof. CHAN Kwok Sum July 25, 2018

July 25, 2018

Dear Kwant Developer, When we use plot to plot a 3D system, is it possible to remove, the x, y, z axes in the final figure? In 2D, no x, y axes is shown. It is nice to have this flexibility. KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

2 2

Finding hamiltonian of system (error in user defined function 'onsite')
by Shivang Agarwal July 6, 2018

July 6, 2018

Hello All, I want to obtain the hamiltonian for my system, for which I am using the *sys.hamiltonian_submatrix()* command, but I get the following error. *UserCodeError: Error occurred in user-supplied value function "onsite".* Below is the code that I am using. *lat = kwant.lattice.honeycomb(a = a)* *p, q = lat.sublattices* *def make_system():* * def hopping(sitei, sitej, phi, salt):* * xi, yi = sitei.pos* * xj, yj = sitej.pos* * return -t * np.exp(-0.5j * phi * (xi - xj) * (yi + yj))* * def onsite(site, phi, salt):* * x, y = site.pos* * return 0* * def central_region(pos):* * x, y = pos* * return abs(x) < 2*a and abs(y) < 3*a* * sys = kwant.Builder()* * sys[lat.shape(central_region, (0, 0))] = onsite* * sys[lat.neighbors()] = hopping* * sym = kwant.TranslationalSymmetry((-a, 0))* * lead = kwant.Builder(sym)* * lead[lat.shape(lambda s: abs(s[1]) < 2*a, (0, 0))] = 0* * lead[lat.neighbors()] = hopping* * sys.attach_lead(lead)* * sys.attach_lead(lead.reversed())* * return sys.finalized()* *sys = make_system()* *sparse_mat = sys.hamiltonian_submatrix() ----> Throws the error* What confuses me is that the code works fine (when I do further calculations on sys) if I comment the *hamitonian_submatrix()* command but throws up the error otherwise. That made me think that the code itself should be correct, but I could not figure out why that line gives an error. I would be glad if someone can help me out with the same. Any help will be much appreciated! Sincerely, Shivang Agarwal -- *Shivang Agarwal* Junior Undergraduate Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451

2 1